Brownian Motions on Metric Graphs

Details Brownian Motions on Metric Graphs Brownian Motions on Metric Graphs

2011-02-24

arxiv.org/abs/1102.4937v2

Mathematics

Probability

35 pages, 7 figures. Revised version of our article 1102.4937. arXiv admin note: substantial text overlap with arXiv:1012.0739

Scientific paper

Brownian motions on a metric graph are defined. Their generators are
characterized as Laplace operators subject to Wentzell boundary at every
vertex. Conversely, given a set of Wentzell boundary conditions at the vertices
of a metric graph, a Brownian motion is constructed pathwise on this graph so
that its generator satisfies the given boundary conditions.

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